1. Technical Field
The present invention relates to a public key cryptosystem using finite non abelian groups and, in particular, to a method of generating finite non abelian groups, an implementation of efficient public key cryptosystem using the non abelian groups and an application method thereof.
2. Background Art
A conventional or symmetric cryptosystem is a system for encrypting and decrypting a document by using a secret key and has disadvantages that there is difficulty in administration of the secret key and a digital signature can not be appended to a message to be transmitted since each of users must have identical secret key.
A public key cryptosystem introduced by Diffie and Hellman in 1976 to provide a new adventure in modem cryptology is a system using a public key and a secret key, in which the public key is publicly known so as to be used by anyone and the secret key is kept by users so that non-public exchange of message is enabled between users having the public key.
Conventionally, RSA encryption scheme using difficult factorization problem of a composite number and ElGamal-type cryptosystem using Discrete Logarithm Problem (DLP) were used. Recently, a braid operation cryptosystem using difficult conjugacy problem in non abelian groups is developed. A public key cryptosystem using elliptic curve is disclosed in “Public key cryptosystem with an elliptic curve” of U.S. Pat. No. 5,272,755 registered on Dec. 21, 1993, and a braid operation cryptosystem using conjugacy problem is disclosed in “New public key cryptosystem using braid group” published on an article book of Advances in Cryptology Crypto 2000 by K. H. Ko, et al. on August 2000.
In case of using the Discrete Logarithm Problem such as ElGamal cipher in Zp, the size of group and key is increased in finite field, which is an abelian group, due to the development of efficient algorithm such as index calculus. Therefore, to solve these problems, a public key cryptosystem must be suggested which can avoid the conventional algorithm for solving the Discrete Logarithm Problem and sufficiently stably maintain the group and key.